Polytope of Type {2,2,57,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,57,4}*1824
if this polytope has a name.
Group : SmallGroup(1824,1247)
Rank : 5
Schlafli Type : {2,2,57,4}
Number of vertices, edges, etc : 2, 2, 57, 114, 4
Order of s₀s₁s₂s₃s₄ : 114
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   19-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,77)(10,79)(11,78)(12,80)(13,73)(14,75)(15,74)(16,76)(17,69)
(18,71)(19,70)(20,72)(21,65)(22,67)(23,66)(24,68)(25,61)(26,63)(27,62)(28,64)
(29,57)(30,59)(31,58)(32,60)(33,53)(34,55)(35,54)(36,56)(37,49)(38,51)(39,50)
(40,52)(41,45)(42,47)(43,46)(44,48);;
s3 := ( 5, 9)( 6,10)( 7,12)( 8,11)(13,77)(14,78)(15,80)(16,79)(17,73)(18,74)
(19,76)(20,75)(21,69)(22,70)(23,72)(24,71)(25,65)(26,66)(27,68)(28,67)(29,61)
(30,62)(31,64)(32,63)(33,57)(34,58)(35,60)(36,59)(37,53)(38,54)(39,56)(40,55)
(41,49)(42,50)(43,52)(44,51)(47,48);;
s4 := ( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)
(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)
(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)
(69,72)(70,71)(73,76)(74,75)(77,80)(78,79);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!(1,2);
s1 := Sym(80)!(3,4);
s2 := Sym(80)!( 6, 7)( 9,77)(10,79)(11,78)(12,80)(13,73)(14,75)(15,74)(16,76)
(17,69)(18,71)(19,70)(20,72)(21,65)(22,67)(23,66)(24,68)(25,61)(26,63)(27,62)
(28,64)(29,57)(30,59)(31,58)(32,60)(33,53)(34,55)(35,54)(36,56)(37,49)(38,51)
(39,50)(40,52)(41,45)(42,47)(43,46)(44,48);
s3 := Sym(80)!( 5, 9)( 6,10)( 7,12)( 8,11)(13,77)(14,78)(15,80)(16,79)(17,73)
(18,74)(19,76)(20,75)(21,69)(22,70)(23,72)(24,71)(25,65)(26,66)(27,68)(28,67)
(29,61)(30,62)(31,64)(32,63)(33,57)(34,58)(35,60)(36,59)(37,53)(38,54)(39,56)
(40,55)(41,49)(42,50)(43,52)(44,51)(47,48);
s4 := Sym(80)!( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)
(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)
(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)
(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79);
poly := sub<Sym(80)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope